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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 311696.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 311696.bf1 | 311696bf2 | \([0, -1, 0, -2454404, -944472164]\) | \(3605503844327632/1235344971091\) | \(560253176916721421056\) | \([]\) | \(11197440\) | \(2.6832\) | |
| 311696.bf2 | 311696bf1 | \([0, -1, 0, -1007244, 389364076]\) | \(249190874485072/45906091\) | \(20819312762381056\) | \([]\) | \(3732480\) | \(2.1339\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 311696.bf do not have complex multiplication.Modular form 311696.2.a.bf
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
